A Fiedler Vector Scoring Approach for Novel RNA Motif Selection

Abstract

Novel RNA motif design is of great practical importance for technology and medicine. Increasingly, computational design plays an important role in such efforts. Our coarse-grained RAG (RNA-As-Graphs) framework offers strategies for enumerating the universe of RNA 2D folds, selecting “RNA-like” candidates for design, and determining sequences that fold onto these candidates. In RAG, RNA secondary structures are represented as tree or dual graphs. Graphs with known RNA structures are called “existing”, and the others are labeled “hypothetical”. By using simplified features for RNA graphs, we have clustered the hypothetical graphs into “RNA-like” and “non-RNA-like” groups and proposed RNA-like graphs as candidates for design. Here, we propose a new way of designing graph features by using Fiedler vectors. The new features reflect graph shapes better, and they lead to a more clustered organization of existing graphs. We show significant increases in K-means clustering accuracy by using the new features (e.g., up to 95% and 98% accuracy for tree and dual graphs, respectively). In addition, we propose a scoring model for top graph candidate selection. This scoring model allows users to set a threshold for candidates, and it incorporates weighing of existing graphs based on their corresponding number of known RNAs. We include a list of top scored RNA-like candidates, which we hope will stimulate future novel RNA design.

RNA-As-Graphs Motif Atlas—Dual Graph Library of RNA Modules and Viral Frameshifting-Element Applications

“…Besides our 2004 graph classification [ 28 ], we proposed an extended list of 78,742 RNA-like candidates out of the 110,667 enumerated dual graphs (2–9 vertices) in 2021, using Fiedler vector based graph feature selection and unsupervised K-means clustering ( Table 1 ) [ 16 ]. Of this list, we find that 167 of the current 182 existing dual graphs (2–9 vertices) were indeed correctly classified as RNA-like (91.8% accuracy), and within the 94 newly found existing dual graphs, 85 were RNA-like (90.4%).…”

“…Among these, only a small portion correspond to real RNA molecules discovered, and we call these “existing”. The remaining graphs are “hypothetical”, and can be further divided into “RNA-like” and “non RNA-like”, by graph feature selection and clustering [ 15 , 16 ]. The “RNA-like” graphs are more likely to be found in nature, as our studies have shown (see also later in this manuscript) [ 15 ].…”

Automatic generation of pseudoknotted RNAs taxonomy

“…However, using it alone is insufficient to distinguish graphs. As proposed in [ 36 ], to develop characteristics that better reflect the graph topology, two features, s and e , are defined as follows: Calculate the normalized Fiedler vector of the Laplacian matrix L ; Sort the Fiedler vector components in ascending order and denote the ordered components ; Scale each to be ; Perform linear regression on the points to obtain slope s and mean squared error e . We computed the dual graphs of all the molecules of the benchmark and the corresponding s and e features.…”

“…In particular, they defined two features, based on the Laplacian matrix, that reflect the graph topology of a structure. Using these features it is possible to define a distance between two structures [ 36 ].…”

Network Algorithms for Intelligent Evaluation of Composition in Middle School English Cloud Classrooms

“…Step four is to calculate the composition score based on the level and grammar weight of the composition (Zhu & Schlick, 2021). The calculation is shown in ( 16).…”